The ground state degeneracy of an $SU(N)_k$ topological phase with $n$ quasiparticle excitations is relevant quantity for quantum computation, condensed matter physics, and knot theory. It is an open question to find a closed formula for this degeneracy for any $N \> 2$. Here we present the problem in an explicit combinatorial way and analyze the case N=3. While not finding a complete closed-form solution, we obtain generating functions and solve some special cases.

}, url = {http://arxiv.org/abs/1009.0114v1}, author = {Stephen P. Jordan and Toufik Mansour and Simone Severini} }